WEBVTT 1 00:00:00.080 --> 00:00:03.359 So picture this. You're playing a game and you round 2 00:00:03.439 --> 00:00:07.240 a corner in some dark digital dungeon and boom and 3 00:00:07.480 --> 00:00:09.119 enemy suddenly springs an ambush. 4 00:00:09.160 --> 00:00:11.480 Oh yeah, your heart just completely jumps into your throat. 5 00:00:11.359 --> 00:00:13.279 Right, And in that split second, you know, you're not 6 00:00:13.359 --> 00:00:16.640 thinking about code or like pixels on a screen. 7 00:00:16.800 --> 00:00:17.480 Oh of course not. 8 00:00:17.600 --> 00:00:20.399 You're just thinking, wow, that felt so real. Because we 9 00:00:20.480 --> 00:00:24.280 play these games expecting this organic spontaneity, right, We really 10 00:00:24.320 --> 00:00:26.679 want that digital world to feel alive, we do. 11 00:00:27.039 --> 00:00:31.960 But the truth is that organic feeling is entirely fabricated, 12 00:00:32.039 --> 00:00:35.479 like completely, when you actually step behind the curtain of 13 00:00:35.600 --> 00:00:39.920 game development, all that spontaneity just vanishes. You're looking at 14 00:00:39.960 --> 00:00:44.399 this landscape of cold, hard, purely deterministic code. 15 00:00:44.159 --> 00:00:46.000 Which is so wild to think about. 16 00:00:46.119 --> 00:00:49.000 It is because computers are well, they're rigid machines. You 17 00:00:49.119 --> 00:00:52.479 literally cannot be spontaneous. Everything you feel in that dungeon 18 00:00:52.880 --> 00:00:55.560 is just a meticulously crafted mathematical illusion. 19 00:00:56.039 --> 00:00:59.439 And today we are ripping open that code to see 20 00:00:59.479 --> 00:01:02.759 exactly how developers pull off that trick. We are doing 21 00:01:02.840 --> 00:01:07.040 a deep dive into this brilliant textbook. It's called Algorithms 22 00:01:07.040 --> 00:01:11.079 and Networking for Computer Games by Juni Smed and Harriet Conan. 23 00:01:11.239 --> 00:01:13.079 It's a fascinating read, it really is. 24 00:01:13.680 --> 00:01:16.719 And our mission today is to figure out how programmers 25 00:01:16.760 --> 00:01:21.040 manipulate math and psychology to trick your brain. We're going 26 00:01:21.120 --> 00:01:23.560 to start from the foundational rules of play and go 27 00:01:23.640 --> 00:01:26.480 all the way down to the invisible algorithms that basically 28 00:01:26.560 --> 00:01:27.760 manufacture chaos. 29 00:01:28.120 --> 00:01:30.480 Yeah, and to understand the math, we first have to 30 00:01:30.519 --> 00:01:33.280 agree on what we're actually trying to simulate, right, right, 31 00:01:33.519 --> 00:01:35.959 Because when you strip away the high resolution graphics and 32 00:01:36.000 --> 00:01:39.959 you know, the fancy haptic feedback controllers, Smed and Hakonan 33 00:01:40.120 --> 00:01:44.359 argue that an interactive world requires one specific crucial ingredient 34 00:01:44.719 --> 00:01:47.000 to separate it from just a static puzzle. 35 00:01:46.799 --> 00:01:48.560 And that ingredient unpredictability. 36 00:01:48.599 --> 00:01:51.040 Okay, let's unpack this because the book uses a really 37 00:01:51.079 --> 00:01:54.680 specific word here, which is conflict. Yes, conflict, And when 38 00:01:54.719 --> 00:01:58.480 I hear conflict, my mind immediately goes to like fighting 39 00:01:58.560 --> 00:02:01.920 a digital dragon or racing against a rival car. But 40 00:02:02.079 --> 00:02:06.120 the authors argue it's actually way broader than that, much brighter. Yeah, 41 00:02:06.280 --> 00:02:10.280 because think about a Sunday crossword puzzle, right. It's challenging, 42 00:02:10.360 --> 00:02:13.000 it has rules, it has a goal, but is it 43 00:02:13.039 --> 00:02:13.479 a game. 44 00:02:13.919 --> 00:02:18.120 Well, by the strict definitions used in game architecture, a 45 00:02:18.159 --> 00:02:21.800 standard crossword puzzle is not actually a game. Wait really yeah, 46 00:02:21.840 --> 00:02:24.879 because it lacks non determinism. A crossword puzzle just sits there. 47 00:02:25.240 --> 00:02:28.159 It doesn't fight back, you know, doesn't adapt. 48 00:02:27.800 --> 00:02:28.360 To your choices. 49 00:02:28.560 --> 00:02:29.120 Okay, I see. 50 00:02:29.199 --> 00:02:32.199 So conflict in this specific context means you are facing 51 00:02:32.240 --> 00:02:37.080 an opposing force or some random process that actively obstructs you. 52 00:02:37.280 --> 00:02:39.240 Right, So if you add a ticking timer to that 53 00:02:39.319 --> 00:02:41.560 crossword or I don't know, you're raising a friend to 54 00:02:41.560 --> 00:02:42.599 finish it first. 55 00:02:42.400 --> 00:02:45.919 Suddenly have non determinism. Exactly, You've injected chaos, and now 56 00:02:45.960 --> 00:02:46.479 you have game. 57 00:02:46.639 --> 00:02:49.599 Okay, So in a single player experience, developers have to 58 00:02:49.719 --> 00:02:54.120 artificially inject that chaos. They have to simulate an opposing 59 00:02:54.199 --> 00:02:57.520 force using AI, which the authors call synthetic players. 60 00:02:57.599 --> 00:02:58.639 Right, synthetic players. 61 00:02:58.800 --> 00:03:00.960 But here is the most counter intuitive part of this 62 00:03:01.000 --> 00:03:04.680 whole illusion. For me, to make an AI opponent feel 63 00:03:04.719 --> 00:03:09.240 like a real, living human, developers actually have to break it. Yes, 64 00:03:09.319 --> 00:03:11.879 they have to make the AI significantly worse. 65 00:03:12.240 --> 00:03:15.280 Well, you have to consider what computers are actually capable of, right, 66 00:03:15.360 --> 00:03:19.520 Like a machine can calculate your character's exact coordinates aim 67 00:03:19.599 --> 00:03:23.199 with pixel perfect precision and just eliminate you the exact 68 00:03:23.199 --> 00:03:24.879 millisecond you enter its line of sight. 69 00:03:24.960 --> 00:03:26.919 Right, It's basically the Terminator exactly. 70 00:03:27.159 --> 00:03:31.479 It possesses superhuman perfection, but playing against flawless perfection is 71 00:03:31.599 --> 00:03:36.080 incredibly boring and frustrating. Completely, it feels robotic, and it 72 00:03:36.159 --> 00:03:39.719 instantly shatters that illusion of playing against a living, breathing 73 00:03:39.840 --> 00:03:41.159 entity in a shared space. 74 00:03:41.520 --> 00:03:44.199 So it's all about simulating human flaws. And there is 75 00:03:44.240 --> 00:03:47.960 this amazing specific detail from the text about how developers 76 00:03:48.000 --> 00:03:48.560 engineer this. 77 00:03:48.680 --> 00:03:49.639 Oh the reaction time. 78 00:03:49.800 --> 00:03:52.800 Yes, when you take a synthetic player by surprise, say 79 00:03:52.840 --> 00:03:55.479 you flank an enemy in a shooter game, the programmers 80 00:03:55.520 --> 00:03:58.599 hard code a deliberate zero point two to zero point 81 00:03:58.599 --> 00:04:02.000 four second reaction time delay before the AI is even 82 00:04:02.000 --> 00:04:02.960 allowed to shoot back. 83 00:04:03.240 --> 00:04:06.840 Yeah, and that specific window of time is absolutely no accident. 84 00:04:07.599 --> 00:04:11.240 It simulates the cognitive processing time of a human being. 85 00:04:11.520 --> 00:04:13.840 It basically mimics panic, panick. 86 00:04:13.960 --> 00:04:14.159 Right. 87 00:04:14.240 --> 00:04:16.800 Yeah, So when you surprise an enemy and they freeze 88 00:04:16.839 --> 00:04:19.959 for like a third of a second before scrambling for cover, 89 00:04:20.480 --> 00:04:23.439 your brain subconsciously registers the ODEA. 90 00:04:23.199 --> 00:04:24.560 Loop, the Obie loop. 91 00:04:24.639 --> 00:04:29.120 Yeah, observe orient decide act, you recognize that slight hesitation 92 00:04:29.160 --> 00:04:31.680 as human cognition, and the illusion holds. 93 00:04:31.920 --> 00:04:36.079 Wow. But this introduces a massive headache for the game designers, 94 00:04:36.079 --> 00:04:36.519 doesn't it. 95 00:04:36.560 --> 00:04:37.759 Oh a huge one. 96 00:04:37.600 --> 00:04:41.959 Because if you program these synthetic players to act somewhat unpredictably, 97 00:04:42.240 --> 00:04:44.639 and then you give the actual human player the freedom 98 00:04:44.680 --> 00:04:47.040 to do literally whatever they want, how on earth do 99 00:04:47.079 --> 00:04:49.800 you guarantee the game still tells a cohesive story. 100 00:04:49.920 --> 00:04:52.480 Well, you've hit on what the authors called the narrative paradox. 101 00:04:52.839 --> 00:04:55.959 It is the central tension in all interactive storytelling. 102 00:04:55.639 --> 00:04:56.639 A narrative paradox. 103 00:04:56.759 --> 00:04:57.040 Yeah. 104 00:04:57.079 --> 00:04:59.519 So, on one side of the scale you have plot coherence, 105 00:04:59.639 --> 00:05:02.120 the there's in the designers. They want to deliver a 106 00:05:02.199 --> 00:05:05.879 well paced, dramatic, emotionally resonant story. 107 00:05:05.639 --> 00:05:07.079 Like a movie exactly. 108 00:05:07.759 --> 00:05:11.800 But on the other side you have character believability and 109 00:05:12.000 --> 00:05:15.560 player agency. You need the player and the AI to 110 00:05:15.680 --> 00:05:18.160 have the actual freedom to ma choices. 111 00:05:17.839 --> 00:05:20.279 Because if I have total freedom, I might just decide 112 00:05:20.319 --> 00:05:23.040 to wander off into the woods to pick digital mushrooms 113 00:05:23.079 --> 00:05:26.000 and completely ignore the terrifying dragon that's supposed to be 114 00:05:26.000 --> 00:05:27.399 attacking the castle. 115 00:05:27.279 --> 00:05:29.759 Right, and then the pacing is completely ruined. The story 116 00:05:29.839 --> 00:05:30.759 just grinds. 117 00:05:30.399 --> 00:05:30.920 To a halt. 118 00:05:31.000 --> 00:05:32.000 So how do they fix that? 119 00:05:32.360 --> 00:05:35.959 So the industry generally tackles this tension from two different directions. 120 00:05:36.360 --> 00:05:40.040 The first is a character centric approach. Okay, here, the 121 00:05:40.079 --> 00:05:44.959 AI characters are highly autonomous. They act on their own program, desires, 122 00:05:45.000 --> 00:05:49.480 and needs, and sometimes they even use a hybrid communication system. 123 00:05:49.519 --> 00:05:50.399 Wait, what does that mean. 124 00:05:50.839 --> 00:05:54.160 Well, they speak in character to the player, but simultaneously 125 00:05:54.519 --> 00:05:57.439 they send out of character signals to the game's background 126 00:05:57.519 --> 00:06:01.360 systems to try gently nudge the plot forward organically. 127 00:06:01.519 --> 00:06:02.680 Oh that's clever, it is. 128 00:06:02.759 --> 00:06:04.720 The story basically emerges from the bottom up. 129 00:06:04.920 --> 00:06:07.120 But the problem with the bottom up approach is that 130 00:06:07.160 --> 00:06:10.079 it can quickly turn into the chaos of everyday life. Right, 131 00:06:10.439 --> 00:06:14.639 real life isn't inherently structured like a three act cinematic blockbuster. 132 00:06:14.920 --> 00:06:16.120 No, it definitely isn't. 133 00:06:16.199 --> 00:06:19.759 So the alternative is the author centric approach, which relies 134 00:06:19.800 --> 00:06:22.160 on something called an invisible drama manager. 135 00:06:22.360 --> 00:06:24.240 Yes, the drama manager, which I love. 136 00:06:24.560 --> 00:06:27.439 Think of it like a stage director secretly walking among 137 00:06:27.480 --> 00:06:32.000 the actors, whispering in their ears, completely unseen by the audience. 138 00:06:32.240 --> 00:06:33.360 That's a perfect way to put it. 139 00:06:33.680 --> 00:06:36.879 The drama manager is constantly running math in the background, 140 00:06:37.279 --> 00:06:40.120 monitoring metrics like player tension and pacing. 141 00:06:40.199 --> 00:06:42.240 So that's washing what I do constantly. 142 00:06:42.439 --> 00:06:45.079 If the algorithm's determined you've been wandering the woods picking 143 00:06:45.120 --> 00:06:47.959 mushrooms for way too long and the tension is dropping, 144 00:06:48.279 --> 00:06:52.079 the drama manager whispers to the AI enemies to spawn 145 00:06:52.160 --> 00:06:54.519 an ambush just out of your line of sight. 146 00:06:54.360 --> 00:06:56.279 To get my heart rate back up exactly. 147 00:06:56.720 --> 00:07:00.680 Or conversely, if you are low on health and completely overwhelmed, 148 00:07:00.920 --> 00:07:03.120 it tells the enemies to pull back a bit or 149 00:07:03.120 --> 00:07:06.240 to miss their shots. It subtly manipulates the parameters of 150 00:07:06.279 --> 00:07:09.399 the world to push you toward the intended emotional beats. 151 00:07:09.639 --> 00:07:13.360 But even with a brilliant invisible director, the developers still 152 00:07:13.360 --> 00:07:16.439 have to physically build the paths the story can take. 153 00:07:16.600 --> 00:07:19.720 Right they do, and the text maps out game stories 154 00:07:19.800 --> 00:07:22.759 using these geometrical graphs. The most basic one is just 155 00:07:22.839 --> 00:07:26.120 a linear story. Episode A always leads to episode B, 156 00:07:26.240 --> 00:07:28.680 which leads to episode C. It's just a straight line. 157 00:07:28.800 --> 00:07:32.240 Yeah, and linear development is incredibly cost effective, but it 158 00:07:32.279 --> 00:07:36.079 offers almost zero agency. You're essentially just walking through a movie, right. 159 00:07:36.439 --> 00:07:40.360 The theoretical opposite of that is a fully branching structure 160 00:07:40.680 --> 00:07:44.680 where every single choice you make leads to a completely different, 161 00:07:44.879 --> 00:07:46.759 unique continuation of the game. 162 00:07:46.639 --> 00:07:49.319 Which sounds like the holy grail of gaming until you 163 00:07:49.399 --> 00:07:52.000 actually do the math on the combinatorial explosion. 164 00:07:52.040 --> 00:07:53.199 Oh, the math is terrifying. 165 00:07:53.360 --> 00:07:55.519 It really is. Let's say you have a scene with 166 00:07:55.639 --> 00:07:58.920 three dialogue choices, and each of those choices leads to 167 00:07:59.079 --> 00:08:02.319 three entirely new scenarios. By the time you reach the 168 00:08:02.399 --> 00:08:05.120 fourth major decision point in the game, you aren't programming 169 00:08:05.120 --> 00:08:09.000 one game anymore. You're programming eighty one completely different games. 170 00:08:09.199 --> 00:08:12.160 You'd have studio spending twelve years and half a billion 171 00:08:12.240 --> 00:08:14.759 dollars just to make a five hour campaign. 172 00:08:15.120 --> 00:08:19.680 It's completely unsustainable. So developers rely on a highly calculated 173 00:08:19.720 --> 00:08:24.319 compromise called parallel pass. Parallel pad right, the story branch 174 00:08:24.360 --> 00:08:26.560 is out for a while, allowing you to make choices, 175 00:08:26.839 --> 00:08:30.399 take different routes, and express your agency. This provides that 176 00:08:30.480 --> 00:08:35.200 crucial illusion of free will ah illusion. But eventually all 177 00:08:35.240 --> 00:08:39.120 those diverged branches are forced to converge back into major, 178 00:08:39.360 --> 00:08:40.720 unavoidable story nodes. 179 00:08:40.919 --> 00:08:43.159 So I might use diplomacy to talk my way past 180 00:08:43.200 --> 00:08:44.799 the guards, and you might just kick the door down 181 00:08:44.879 --> 00:08:48.960 with explosives typical exactly, but thirty minutes later, we both 182 00:08:49.039 --> 00:08:51.279 end up standing in the exact same throne room for 183 00:08:51.320 --> 00:08:53.320 the exact same final boss fight. 184 00:08:53.639 --> 00:08:57.600 Yes, the game just acknowledges are different methods in the dialogue. 185 00:08:57.840 --> 00:09:00.679 It keeps the studio from going bankrupt while letting us 186 00:09:00.679 --> 00:09:03.120 feel like we are the actual authors of our own fate. 187 00:09:03.279 --> 00:09:05.960 So the illusion of free will is maintained by carefully 188 00:09:06.000 --> 00:09:10.240 hidden constraints exactly, And that reliance on nondeterminism, you know, 189 00:09:10.399 --> 00:09:15.120 on generating a feeling of unpredictable chaos within strict mathematical limits, 190 00:09:15.799 --> 00:09:18.879 brings us to the very bedrock of how a computer operates. 191 00:09:20.039 --> 00:09:22.559 And here's where it gets really interesting for me, oh 192 00:09:22.559 --> 00:09:26.399 for sure, Because whether we are talking about parallel story branches, 193 00:09:26.600 --> 00:09:29.960 or that zero point three second reaction delay for the AI, 194 00:09:30.679 --> 00:09:34.519 or even simulating a dice roll, games need randomness to function. 195 00:09:34.320 --> 00:09:35.480 They desperately need it. 196 00:09:35.519 --> 00:09:39.519 But a computer processor is a purely deterministic machine. It 197 00:09:39.720 --> 00:09:43.039 only executes the exact logic gits it is fed. It 198 00:09:43.039 --> 00:09:45.960 cannot flip a coin. True randomness in a computer is 199 00:09:46.000 --> 00:09:46.720 a total myth. 200 00:09:46.919 --> 00:09:50.000 It is developers literally have to fake it. Yeah, they 201 00:09:50.080 --> 00:09:53.759 use algorithms to produce sequences of numbers that just behave unpredictably, 202 00:09:54.120 --> 00:09:56.960 and these fall into two main categories, which are quasi 203 00:09:57.039 --> 00:09:58.120 random and pseudorandom. 204 00:09:58.159 --> 00:09:59.279 Oh hey, let's break this down well. 205 00:09:59.360 --> 00:10:02.000 Quasi random numbers are sequences that actually have a hidden 206 00:10:02.039 --> 00:10:06.000 structural rule, but they just appear random to a naive observer. 207 00:10:06.200 --> 00:10:08.799 Right, So, think of a sequence that alternates strictly between 208 00:10:08.799 --> 00:10:12.279 even and odd numbers, but the numbers themselves jump wildly 209 00:10:12.320 --> 00:10:15.240 across a massive range. Good example, if you just look 210 00:10:15.240 --> 00:10:17.720 at a short sample of that, it feels totally chaotic, 211 00:10:18.080 --> 00:10:20.879 but there's a rigid skeleton holding it together to ensure 212 00:10:21.039 --> 00:10:23.039 an even spread of events over time. 213 00:10:23.720 --> 00:10:26.360 Yeah, and that even spread is really useful for certain 214 00:10:26.440 --> 00:10:30.320 visual rendering tasks. But when we need numbers that pass 215 00:10:30.440 --> 00:10:37.159 rigorous statistical tests for actual chaotic unpredictability, we need pseudorandom 216 00:10:37.320 --> 00:10:38.360 number generators. 217 00:10:38.480 --> 00:10:39.240 Pseudorandom. 218 00:10:39.360 --> 00:10:43.240 Yes, and the foundational algorithm detailed by Smed and hecanin 219 00:10:43.759 --> 00:10:46.879 is the linear congruential method or the LCM. 220 00:10:47.039 --> 00:10:49.600 The LCM now it sounds like high level calculus, but 221 00:10:49.639 --> 00:10:53.000 it's really just a simple mathematical loop built on four parameters. 222 00:10:53.080 --> 00:10:54.519 Right. It is surprisingly simple. 223 00:10:54.600 --> 00:10:56.480 You have the modulus, which we'll call M. You have 224 00:10:56.559 --> 00:11:00.000 the multiplier A, the increment C, and a starting value 225 00:11:00.159 --> 00:11:00.919 which is known as the. 226 00:11:00.879 --> 00:11:04.919 Seed exactly, and the operation itself is just basic arithmetic. 227 00:11:05.320 --> 00:11:08.080 So the algorithm takes your seed value and it multiplies 228 00:11:08.120 --> 00:11:08.519 it by. 229 00:11:08.440 --> 00:11:09.559 A, and then it adds C. 230 00:11:09.960 --> 00:11:11.440 Okay, easy enough, right, But then it. 231 00:11:11.440 --> 00:11:14.720 Divides that total by the modulus M and whatever the 232 00:11:14.720 --> 00:11:17.360 remainder of that division is. That remainder becomes your first 233 00:11:17.399 --> 00:11:21.840 random number, the remainder, right, yeah, Then the algorithm takes 234 00:11:21.840 --> 00:11:24.200 that brand new number, plugs it back into the start 235 00:11:24.200 --> 00:11:26.720 of the formula is the new seed, and runs the 236 00:11:26.840 --> 00:11:27.600 entire loop again. 237 00:11:27.919 --> 00:11:31.120 So picture a clock face. Let's say our modulus is twelve, 238 00:11:31.440 --> 00:11:34.360 so we have a standard twelve hour clock. No matter 239 00:11:34.360 --> 00:11:37.720 how wildly you multiply or add numbers together, when you 240 00:11:37.759 --> 00:11:40.519 divide by twelve and take the remainder, the answer is 241 00:11:40.559 --> 00:11:42.840 just spinning around the dial, right, that's right. It will 242 00:11:42.879 --> 00:11:45.000 always land on a notch between one and twelve. 243 00:11:45.200 --> 00:11:48.840 It's a really elegant way to constrain infinite math into 244 00:11:48.879 --> 00:11:52.840 a usable range. But because it's a closed mathematical loop 245 00:11:52.879 --> 00:11:57.039 operating within that fixed clock face, the sequence of numbers 246 00:11:57.120 --> 00:12:00.919 will eventually run out of unique combinations, it starts repeating 247 00:12:00.919 --> 00:12:01.600 itself exactly. 248 00:12:01.679 --> 00:12:02.279 Oh wow. 249 00:12:02.480 --> 00:12:05.279 The length of this unique sequence before it finally loops 250 00:12:05.399 --> 00:12:08.360 is called the period. So if your modulus is twelve, 251 00:12:08.720 --> 00:12:12.000 the absolute maximum period you can achieve is twelve numbers. 252 00:12:12.080 --> 00:12:16.360 And a repeating loop is the death of unpredictability. Like 253 00:12:16.440 --> 00:12:18.759 if I'm playing a digital card game and I realize 254 00:12:18.799 --> 00:12:21.159 the deck is dealing me the exact same sequence of 255 00:12:21.200 --> 00:12:25.320 hands every twelve rounds, the illusion completely shatters. It does 256 00:12:25.480 --> 00:12:27.639 I can predict the future. The game is basically broken 257 00:12:27.679 --> 00:12:28.639 at that point. 258 00:12:28.840 --> 00:12:31.440 So to prevent the player from ever seeing the loop, 259 00:12:31.840 --> 00:12:37.440 developers use unimaginably massive numbers for the modulus. But you 260 00:12:37.440 --> 00:12:38.799 can't just pick any large number. 261 00:12:38.840 --> 00:12:39.159 Why not? 262 00:12:39.360 --> 00:12:44.600 You want a very specific mathematical structure, ideally a prime number. Specifically, 263 00:12:44.639 --> 00:12:46.840 developers often use Mrsenne primes. 264 00:12:47.159 --> 00:12:49.440 Okay, wait, so why a prime number? If I just 265 00:12:49.480 --> 00:12:52.080 pick a huge round number like a billion, doesn't that 266 00:12:52.159 --> 00:12:54.759 just give me a billion notches on my clock? Face? 267 00:12:54.960 --> 00:12:59.519 It does, but it introduces this problem of coprimality to primality. Yeah, 268 00:12:59.879 --> 00:13:03.159 your modulus clod phase shares a common divisor with your multiplier, 269 00:13:03.600 --> 00:13:05.279 the math will start skipping notches. 270 00:13:05.399 --> 00:13:06.360 Oh I think I see. 271 00:13:06.480 --> 00:13:09.799 Imagine a twelve hour clock and your multiplier forces you 272 00:13:09.840 --> 00:13:13.480 to jump by threes. You hit three, six, nine, twelve, 273 00:13:13.519 --> 00:13:14.960 and then you're right back where you started. 274 00:13:15.159 --> 00:13:18.360 You only generated four unique numbers, even though your clock 275 00:13:18.399 --> 00:13:19.559 has twelve spaces. 276 00:13:19.759 --> 00:13:23.039 Exactly, by using a massive prime number for the modulus, 277 00:13:23.440 --> 00:13:26.480 you guarantee it shares no divisors with your other parameters. 278 00:13:26.919 --> 00:13:29.799 It forces the algorithm to step on every single unique 279 00:13:29.840 --> 00:13:31.879 notch before it's ever allowed to loop. 280 00:13:32.159 --> 00:13:36.279 That is genuinely brilliant, and the text mentions a common 281 00:13:36.440 --> 00:13:39.960 Mersen prime used is two to the thirty first power 282 00:13:40.080 --> 00:13:43.879 minus one, which is over two point one billion massive. 283 00:13:44.519 --> 00:13:48.039 So the clockface has two point one billion unique notches, 284 00:13:48.440 --> 00:13:51.399 and because it's prime, we hit every single one. The 285 00:13:51.440 --> 00:13:56.000 sequence still repeats eventually, but the period is so incomprehensibly 286 00:13:56.120 --> 00:13:59.080 long that a human playing the game will literally never 287 00:13:59.159 --> 00:14:01.000 live long enough to notice the pattern. 288 00:14:01.360 --> 00:14:05.080 True, but there is a huge vulnerability in this closed loop. 289 00:14:05.159 --> 00:14:07.879 Wait really, because I'm looking at this formula, MA and 290 00:14:07.960 --> 00:14:11.080 C are hard coded by the developer. The only variable 291 00:14:11.080 --> 00:14:13.960 that starts the whole chain reaction is the seed exactly. 292 00:14:14.039 --> 00:14:15.960 So if I turn on my console, boot up the game, 293 00:14:16.000 --> 00:14:18.360 and the default seed value is just the number one 294 00:14:18.399 --> 00:14:21.159 every single time. Wouldn't the math just spit out the 295 00:14:21.200 --> 00:14:24.399 exact same sequence of random events every time I play yes? 296 00:14:25.039 --> 00:14:27.519 The game would play out exactly the same way. The 297 00:14:27.559 --> 00:14:30.600 ambush that terrified you in your first playthrough would happen 298 00:14:30.639 --> 00:14:33.799 at the exact same millisecond in your second play through. 299 00:14:33.879 --> 00:14:36.600 That ruins everything, right, So to fix this, developers have 300 00:14:36.639 --> 00:14:40.720 to inject a tiny spark of real world physical chaos 301 00:14:41.080 --> 00:14:44.720 to kickstart the math. They will program the game to 302 00:14:44.799 --> 00:14:49.679 fetch its starting seed from highly variable, totally unpredictable sources 303 00:14:49.879 --> 00:14:51.720 from outside the game's. 304 00:14:51.399 --> 00:14:55.279 Code, like grabbing the computer's internal clock time down to 305 00:14:55.279 --> 00:14:59.120 the microscopic millisecond of the exact moment you press start 306 00:14:59.279 --> 00:15:02.799 yes exactly, or pulling data from the tiny erratic temperature 307 00:15:02.840 --> 00:15:06.559 fluctuations of the CPU, or even the microscopic tremor of 308 00:15:06.559 --> 00:15:09.679 your hand on the computer mounts. They literally capture a 309 00:15:09.759 --> 00:15:13.559 fraction of physical reality to see the digital illusion. 310 00:15:14.360 --> 00:15:15.960 That is amazing, it's really cool. 311 00:15:16.200 --> 00:15:18.600 But once you've seeded the algorithm and it's churning out 312 00:15:18.600 --> 00:15:21.960 billions of numbers, you still have a massive problem. Another one, Yeah, 313 00:15:22.000 --> 00:15:23.639 how do you actually know the illusion works, you have 314 00:15:23.720 --> 00:15:27.000 to test it rigorously, right, and the text outlines several 315 00:15:27.080 --> 00:15:30.840 empirical tests, like the poker test, where yougroup the generator's 316 00:15:30.840 --> 00:15:33.240 output into hands of five and see if they match 317 00:15:33.279 --> 00:15:35.960 the real world statistical probability of drawing a full house 318 00:15:36.039 --> 00:15:39.120 or a flush. That makes sense, But the most revealing 319 00:15:39.279 --> 00:15:43.799 diagnostic for the linear congruential method is called the spectral test. 320 00:15:44.200 --> 00:15:46.840 The spectral test, Okay, it sounds like ghost hunting. 321 00:15:46.679 --> 00:15:49.720 It does, but it's actually a highly visual geometric test. 322 00:15:49.919 --> 00:15:53.720 So imagine taking the sequence of number your algorithm produces, yeah, 323 00:15:53.799 --> 00:15:57.399 grouping them into pairs, and plotting those pairs as x 324 00:15:57.440 --> 00:15:59.919 and y coordinates on a massive two. 325 00:16:00.679 --> 00:16:01.600 Okay, I'm picturing it. 326 00:16:01.960 --> 00:16:06.799 If your generator is producing true chaotic randomness, that graph 327 00:16:06.879 --> 00:16:10.519 should look like pure uniform television static. There should be 328 00:16:10.519 --> 00:16:11.519 absolutely no pattern. 329 00:16:11.679 --> 00:16:15.039 But the LCM isn't true chaos. It's built on fixed 330 00:16:15.120 --> 00:16:16.639 multiplication and addition. 331 00:16:16.519 --> 00:16:20.240 Exactly because of that linear mathematical relationship. If you zoom 332 00:16:20.240 --> 00:16:22.759 out and look at that TV static, you will realize 333 00:16:22.799 --> 00:16:25.720 that dots aren't actually random at all. They align to 334 00:16:25.840 --> 00:16:28.559 form a lattice of perfectly parallel lines. Wow, they are 335 00:16:28.600 --> 00:16:31.440 mathematically tethered together. And if you group the numbers into 336 00:16:31.440 --> 00:16:34.080 triplets and plot them in a three D space, those 337 00:16:34.120 --> 00:16:35.679 lines become parallel planes. 338 00:16:35.840 --> 00:16:38.559 So the illusion has literal seams in it. The randomness 339 00:16:38.600 --> 00:16:40.360 is basically stacked in layers. 340 00:16:40.720 --> 00:16:45.480 Yes, the spectral test measures the distance between those parallel planes. 341 00:16:46.399 --> 00:16:48.799 If the planes are too far apart, it means there 342 00:16:48.840 --> 00:16:52.039 are massive predictable gaps in your random spread, and you 343 00:16:52.039 --> 00:16:55.679 don't want that. No, So a high quality algorithm uses 344 00:16:55.720 --> 00:17:00.399 parameters carefully calibrated to push those planes as tightly together 345 00:17:00.440 --> 00:17:03.720 as possible, basically blurring the lines until the human eye 346 00:17:04.039 --> 00:17:07.440 and statistical analysis only sees pure static. 347 00:17:07.680 --> 00:17:10.240 Okay, So let's say our math past the spectral test. 348 00:17:10.519 --> 00:17:14.039 The algorithm is incredibly robust, and it just generated a 349 00:17:14.160 --> 00:17:18.640 massive pseudo random number, let's say one point eight billion. Okay, 350 00:17:18.720 --> 00:17:21.119 but I'm playing a digital board game and my character 351 00:17:21.160 --> 00:17:24.400 just needs to roll a standard six sided die. How 352 00:17:24.400 --> 00:17:27.319 does the code shrink a massive one point eight billion 353 00:17:27.359 --> 00:17:29.759 output down to a tiny interval of one to six 354 00:17:30.160 --> 00:17:33.160 without destroying the delicate randomness we just engineered. 355 00:17:33.279 --> 00:17:36.039 Well, if you take the lazy route, you absolutely ruin 356 00:17:36.079 --> 00:17:36.359 the die. 357 00:17:36.440 --> 00:17:36.680 Yeah. 358 00:17:36.720 --> 00:17:39.160 Most basic approach, which the text calls the Monte Carlo 359 00:17:39.200 --> 00:17:42.240 method is to just divide your massive random number by six. 360 00:17:42.039 --> 00:17:44.160 And take the remainder like the clock face right. 361 00:17:44.200 --> 00:17:45.839 But this warps the distribution. 362 00:17:45.640 --> 00:17:49.400 Because the maximum limit of your huge random number generator 363 00:17:49.720 --> 00:17:52.000 probably isn't perfectly divisible. 364 00:17:51.519 --> 00:17:52.799 By six exactly. 365 00:17:52.839 --> 00:17:55.480 Think of it like having a pizza with twenty slices 366 00:17:55.880 --> 00:17:58.279 and you need to divide it evenly among six people. 367 00:17:58.680 --> 00:18:01.799 Everyone gets three slices, but you have two slices left. 368 00:18:01.559 --> 00:18:03.200 Over, yep, the remainder. 369 00:18:03.279 --> 00:18:05.839 And if you just hand those remaining slices out to 370 00:18:05.960 --> 00:18:09.039 whoever is closest, two people end up with more pizza. 371 00:18:09.880 --> 00:18:12.400 In the code. That means the numbers one and two 372 00:18:12.559 --> 00:18:15.920 end up with slightly more mathematical real estate than three, four, five, 373 00:18:16.000 --> 00:18:16.559 or six. 374 00:18:16.400 --> 00:18:19.680 Which means the digital die becomes mathematically loaded. Over the 375 00:18:19.680 --> 00:18:22.960 course of thousands of roles, the player will absolutely notice 376 00:18:22.960 --> 00:18:25.319 that they are rolling ones in twos more often. 377 00:18:25.000 --> 00:18:27.119 And it feels completely unfair it does. 378 00:18:27.519 --> 00:18:30.279 So to solve this, developers use something called the Las 379 00:18:30.400 --> 00:18:31.119 Vegas method. 380 00:18:31.480 --> 00:18:34.599 I love the Las Vegas method because it's so uncompromising. 381 00:18:34.640 --> 00:18:39.720 It essentially guarantees a perfectly uniform distribution by simply throwing 382 00:18:39.759 --> 00:18:42.839 the excess pizza slices directly into the trash. 383 00:18:43.000 --> 00:18:46.559 That's pretty much it in terms of the code. If 384 00:18:46.559 --> 00:18:49.640 the algorithm generates a huge number that happens to fall 385 00:18:49.640 --> 00:18:51.799 into that uneven remainder zone at the very top of 386 00:18:51.839 --> 00:18:55.400 its range, the code literally intercepts it. 387 00:18:55.400 --> 00:18:56.279 It just catches it. 388 00:18:56.359 --> 00:18:59.119 Yeah, it discards the number silently and goes right back 389 00:18:59.119 --> 00:19:00.519 to the start of the loop reroll. 390 00:19:01.359 --> 00:19:02.160 It repeats this. 391 00:19:02.160 --> 00:19:06.000 Invisible process in a fraction of a millisecond until it 392 00:19:06.039 --> 00:19:09.759 generates a number that falls cleanly into the perfectly divisible range. 393 00:19:09.720 --> 00:19:12.000 And only then does it show the die roll to 394 00:19:12.039 --> 00:19:12.480 the player. 395 00:19:12.680 --> 00:19:16.839 Yes, it sacrifices precious computing power and time purely to 396 00:19:16.880 --> 00:19:18.519 guarantee absolute fairness. 397 00:19:18.599 --> 00:19:21.359 It's beautiful. But so many game mechanics have nothing to 398 00:19:21.400 --> 00:19:24.519 do with rolling dice, right. They are about managing time 399 00:19:24.599 --> 00:19:27.759 and flow, like when does the next wave of zombies attack? 400 00:19:27.880 --> 00:19:29.319 Or when does a rainstorm start? 401 00:19:29.319 --> 00:19:30.160